Non-Local Sensitivity Analysis and Numerical Homogenization in Optimal Design of Single-Wall Corrugated Board Packaging

Abstract

The optimal selection of the composition of corrugated cardboard dedicated to specific packaging structures is not an easy task. The use of lighter boards saves material, but at the same time increases the risk of not meeting the guaranteed load capacity. Therefore, the answer to the question “in which layer the basis weight of the paper should be increased?” is not simple or obvious. The method proposed here makes it easy to understand which components and to what extent they affect the load-bearing capacity of packages of various dimensions. The use of numerical homogenization allows for a quick transformation of a cardboard sample, i.e., a representative volume element (RVE) into a flat plate structure with effective parameters describing the membrane and bending stiffness. On the other hand, the use of non-local sensitivity analysis makes it possible to find the relationship between the parameters of the paper and the load capacity of the packaging. The analytical procedures presented in our previous studies were used here to determine (1) the edge crush resistance, (2) critical load, and (3) the load capacity of corrugated cardboard packaging. The method proposed here allows for obtaining a comprehensive and hierarchical list of the parameters that play the most important role in the process of optimal packaging design.

Optimal Design of Double-Walled Corrugated Board Packaging

“…This study is a continuation of the work recently presented by Mrówczyński et al [ 2 ]. What distinguishes this work from the previous one is the attention to the effects related to imperfections in the asymmetrical cross section of a five-layer corrugated cardboard.…”

“…Corrugated cardboard is a layered structure whose strength is determined by the individual ply selection and combination, especially given the fact that the mechanical strength of paperboard depends on two characteristic, i.e., the in-plane directions of orthotropy—perpendicular to the main axis of the fluting and parallel to the paperboard fiber alignment machine direction (MD), as well as parallel to the fluting cross direction (CD). This paper presents a critical look at the process of optimal selection of five-layer corrugated cardboard for packaging structures, depending on the paper used, as a continuation of the discussion presented for three-ply cardboard by Mrówczyński et al [ 2 ].…”

Simplified Modelling of the Edge Crush Resistance of Multi-Layered Corrugated Board: Experimental and Computational Study

“…), therefore, the correct modeling of packaging is taking on increasing importance. The optimal design of the corrugated cardboard packages was examined by Mrówczy ński et al [24,25]. The use of recycled fibers in the production of paper and cardboard causes the fibers to become shorter and more brittle after many recovery cycles, and their ability to create a stable network of connections with other fibers keeps getting smaller over time.…”

Influence of Analog and Digital Crease Lines on Mechanical Parameters of Corrugated Board and Packaging

“…The behavior of the cardboard is inextricably linked to its dimensions: a high edge crush strength is crucial in low and stocky boxes, whereas in higher packaging the buckling strength, it is decisive [12][13][14]. The optimal selection of the constituents of corrugated board layers is of major importance for the load-bearing capacity of packages [15,16]. An option is the utilization of lighter boards as well as kraft or recycled papers, which have reduced mechanical parameters, saving material and thus diminishing cost.…”

“…The method of reducing a multilayer structure to a single layer is called homogenization. This process can be undertaken using analytical [35,36] or numerical approaches [15,30,[37][38][39][40][41].…”